1. Field of the Invention
This invention relates to marine seismic exploration and more particularly to the determination of water bottom reflectivities from recorded seismograms for use in dereverberation of seismic data without adversely damaging reflection sequences that have a periodicity close to that of the two-way travel time in water of seismic waves.
2. Background of the Art
In marine seismic exploration, seismic energy is generated by sources towed behind a vessel. The resultant acoustic pressure waves are reflected from the subsurface formations and recorded as seismograms. Typically, the recorded seismograms include noises that obscure the characteristics of the subsurface formations. These noises include water bottom multiples as depicted in FIG. 2 and reverberations as depicted in FIGS. 3 and 4.
As the initial shot pulse travels to the bottom of the water, it is partially transmitted and partially reflected by the water bottom. The portion that is transmitted is reflected by discontinuities beneath the water to become primary reflections that are important for imaging the subsurface of the earth. The reflected part bounces back to the surface where it is again reflected to the water bottom. Once more, part of this pulse passes through the boundary and part is reflected. The process continues indefinitely. Each time a pulse bounces between the surface and the bottom of the water, a pulse emerges from the boundary at the bottom to follow the initial pulse into the section. These multiple pulses are delayed equal time intervals relative to each other, and their amplitudes are successively reduced by the reflection coefficient at the bottom of the water. A similar process happens with the primary reflections that bounce around in the water layer. The net result of this is to produce a seismogram consisting of a single primary followed by a train of equally spaced multiples or reverberations.
The seismic trace that is generated by a shot pulse may be described mathematically as EQU X(t)=S(t)*R(t)*H(t)+N(t) (1)
where X(t) is the recorded signal, S(t) is the source signal, R(t) is a reflectivity sequence characterizing the subsurface of the earth, H(t) is a distortion function and N(t) is additive noise. The noise may be coherent or incoherent.
The distortion function that characterizes reverberations is given by the equation ##EQU1## where H R (t) is the revereberation operator, r is the reflection coefficient at the water bottom, .delta. is the Kronecker delta function, T is the two-way travel time in the water for acoustic waves. In the z-transform domain, the dereverberation operator may be denoted by ##EQU2##
In those circumstances wherein the water bottom is relatively flat, the downward-going reverberation distortion at the shotpoint, and the upward-going reverberation distortion at the detector are approximately the same. Consequently, for a flat water bottom, a total dereverberation operator can be represented by the convolution of the two-point operator at the shotpoint with the two-point operator at the detector. This gives the so-called Backus operator ##EQU3##
U.S. Pat. No. 3,689,874 to Foster et al. discloses a method for dereverberation of the recorded signal using the autocorrelation of the recorded traces. The method assumes that the autocorrelation of the reflectivity and the noise sequences can be characterized as white noise.
U.S. Pat. No. 4,146,871 to Ruehle discloses a method for dereverberation of recorded signals wherein the dereverberation operator is determined by trying different values for the water bottom reflectivity r and the two-way travel time in the water T and, after the best value is determined from a visual inspection of the processed traces, the air guns in the seismic source are fired sequentially to simulate the dereverberation operator.
Deployment of ocean bottom sensors is frequently used for obtaining 3-D seismic data in an area with obstacles that would hinder the use of towed streamers. Such a situation occurs, for example, when data are being acquired in the proximity of production platforms. With ocean bottom sensors, the "ghost" on the recorded sensor data due to a reflection from the water surface occurs at larger times than it does with streamer data: the streamers being typically at depths of less than 10 meters while the ocean bottom sensors may be at depths of tens or hundreds of meters of water. The multiple sensor arrays include pressure sensors (hydrophones) and vertical component sensors. The latter are usually velocity sensors (geophones). If the water bottom reflectivity is known, the pressure and velocity signals may be combined to give the upcoming field. U.S. Pat. No. 5,524,100 issued to Paffenholz describes an arrangement in which multiple-sensor arrays are deployed on the sea bottom. Pressure and velocity seismic signals are combined, the combined signal is transformed into the frequency domain and multiplied by the inverse Backus operator or the combined signal is convolved with the inverse Backus operator, and an optimization algorithm is used to solve for water bottom reflectivity. Pressure and velocity seismic signals are combined, and the combined signal is multiplied by the inverse Backus operator containing the water bottom reflectivity to eliminate first order peg leg multiples.
One of the problems associated with prior art methods is that the determination of the dereverberation operator may be clouded by geologic reflectivity sequences that have the same time delay as the two-way travel time in water. The processing methods are unable to distinguish between spectral notches caused by reverberations and spectral notches caused by subterranean reflections. Consequently, the derverberation operator will also suppress reflection sequences that have the same time delay as the Backus operator and the resulting processed seismic data will be incorrect in that certain reflections associated with subterranean geology will be suppressed, leading to possible misinterpretations of the data. It would be desirable to have a method of dereverberation of marine seismic data that is robust in the presence of such geologic interference. The present invention satisfies the need.